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3 years ago

8

Sara bought a pair of pants that were on sale for 30 percent off of the original price. If the original price of the pants was $

29, what was the sales price of the pants?

1 answer:

Ne4ueva [31]3 years ago

8 0

Answer:

The new cost is $20.30

Step-by-step explanation:

In order to find that, start by taking the original price and multiplying it by what percentage you have to pay. Since it is 30% off, you have to pay 70%

$29*70% = $20.30

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An equilateral is shown inside a square inside a regular pentagon inside a regular hexagon. The square and regular hexagon are s

Kay [80]

Shaded area = area of the hexagon – area of the pentagon + area of the square – area of the equilateral triangle. This can be obtained by finding each shaded area and then adding them.

<h3>Find the expression for the area of the shaded regions:</h3>

From the question we can say that the Hexagon has three shapes inside it,

Pentagon

Square

Triangle

Also it is given that,

An equilateral triangle is shown inside a square inside a regular pentagon inside a regular hexagon.

From this we know that equilateral triangle is the smallest, then square, then regular pentagon and then a regular hexagon.

A pentagon is shown inside a regular hexagon.

Area of first shaded region = Area of the hexagon - Area of pentagon

An equilateral triangle is shown inside a square.

Area of second shaded region = Area of the square - Area of equilateral triangle

The expression for total shaded region would be written as,

Shaded area = Area of first shaded region + Area of second shaded region

Hence,

⇒ Shaded area = area of the hexagon – area of the pentagon + area of the square – area of the equilateral triangle.

Learn more about area of a shape here:

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2 years ago

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A turtle traveled 1/10 miles in 1/2 hour, what was the turtles rate in miles per hour

Ivan

Answer:

.2 mph

Step-by-step explanation:

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3 years ago

A floor rug is rectangular in shape. The width of the rug is 2 ft less than its length. The perimeter of the rug is 36 ft.

Ganezh [65]

Answer

Perimeter of rectangle, P = 2L + 2W

P = 36ft

Width, W

Length, L = W + 2ft

Perimeter of rectangle, P = 2L + 2W

Given; P = 36ft

36ft = 2W + 2(W + 2ft)

36ft = 2W + 2W + 4ft

32ft = 4W

8ft = W

L = W + 2ft

L = 8ft + 2ft

L = 10ft

5 0

3 years ago

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They have a rectangle ABCD as shown below, where AB = 24cm BC = 10cm and AE = 13cm

alex41 [277]

Answer:

A. Area of ABCD = 240 $cm^{2}$

B. 60 cm

C. 36 cm

D. 50 cm

Step-by-step explanation:

Given: AB = 24cm BC = 10cm and AE = 13cm.

A. Since a rectangle is a 2 dimensional figure, it has no volume but area.

So that,

the area of the rectangle ABCD = length x width

= 24 x 10

= 240 $cm^{2}$

B. To calculate the circumference of the BCD triangle, apply the Pythagoras theorem to determine BD.

$BD^{2}$ = $BC^{2}$ + $DC^{2}$

= $10^{2}$ + $24^{2}$

= 676

BD = $\sqrt{676}$

= 26

BD = 26 cm

so that,

the circumference of BCD = 10 + 24 + 26

= 60 cm

C. To calculate the circumference of the BEC triangle,

AC = 26 cm, AE = 13 cm

CE = 26 - 13

= 13 cm

CE = 13 cm

The circumference of the BEC triangle = 13 + 13 + 10

= 36 cm

D. The circumference of the DEC triangle = 13 + 13 + 24

= 50 cm

7 0

3 years ago

A box with a rectangular base and open top must have a volume of 128 f t 3 . The length of the base is twice the width of base.

noname [10]

Answer:

$Width = 4ft$

$Height = 4ft$

$Length = 8ft$

Step-by-step explanation:

Given

$Volume = 128ft^3$

$L = 2W$

$Base\ Cost = \$9/ft^2$

$Sides\ Cost = \$6/ft^2$

Required

The dimension that minimizes the cost

The volume is:

$Volume = LWH$

This gives:

$128 = LWH$

Substitute $L = 2W$

$128 = 2W * WH$

$128 = 2W^2H$

Make H the subject

$H = \frac{128}{2W^2}$

$H = \frac{64}{W^2}$

The surface area is:

Area = Area of Bottom + Area of Sides

So, we have:

$A = LW + 2(WH + LH)$

The cost is:

$Cost = 9 * LW + 6 * 2(WH + LH)$

$Cost = 9 * LW + 12(WH + LH)$

$Cost = 9 * LW + 12H(W + L)$

Substitute: $H = \frac{64}{W^2}$ and $L = 2W$

$Cost =9*2W*W + 12 * \frac{64}{W^2}(W + 2W)$

$Cost =18W^2 + \frac{768}{W^2}*3W$

$Cost =18W^2 + \frac{2304}{W}$

To minimize the cost, we differentiate

$C' =2*18W + -1 * 2304W^{-2}$

Then set to 0

$2*18W + -1 * 2304W^{-2} =0$

$36W - 2304W^{-2} =0$

Rewrite as:

$36W = 2304W^{-2}$

Divide both sides by W

$36 = 2304W^{-3}$

Rewrite as:

$36 = \frac{2304}{W^3}$

Solve for $W^3$

$W^3 = \frac{2304}{36}$

$W^3 = 64$

Take cube roots

$W = 4$

Recall that:

$L = 2W$

$L = 2 * 4$

$L = 8$

$H = \frac{64}{W^2}$

$H = \frac{64}{4^2}$

$H = \frac{64}{16}$

$H = 4$

Hence, the dimension that minimizes the cost is:

$Width = 4ft$

$Height = 4ft$

$Length = 8ft$

8 0

3 years ago